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Question
Prove the following identities:
`cosA/(1 - sinA) = sec A + tan A`
Solution
L.H.S. = `cosA/(1-sinA)`
= `(cosA(1 + sinA))/((1 - sinA)(1 + sinA))`
= `(cosA(1 + sinA))/(1 - sin^2A)`
= `(cosA(1 + sinA))/(cos^2A)`
= `(1 + sinA)/cosA`
= `1/cosA + sinA/cosA`
= sec A + tan A = R.H.S.
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Activity:
L.H.S = `square`
= `square/sintheta + sintheta/costheta`
= `(cos^2theta + sin^2theta)/square`
= `1/(sintheta*costheta)` ......`[cos^2theta + sin^2theta = square]`
= `1/sintheta xx 1/square`
= `square`
= R.H.S
